Cartesian to Polar Converter

Convert Cartesian coordinates (x, y) into polar coordinates (r, θ). See the radius r and angle θ in both degrees and radians, with a coordinate diagram.

Input

Enter values for x and y to convert them into polar coordinates (r, θ).

x coordinate

y coordinate

Result

Polar coordinates (r, θ)

r = 5, θ = 53.130102°

Radius r

Angle θ (degrees)

53.130102°

Angle θ (radians)

0.927295 rad

Angle θ (0 to 360)

53.130102°

The angle is computed with atan2(y, x); its range is greater than minus pi and up to pi. A 0 to 360 degree form is also shown.

How it works

The radius is r = sqrt(x squared + y squared), the distance from the origin.
The angle is theta = atan2(y, x), which distinguishes all four quadrants. Its range is greater than minus pi and up to pi.
Degrees come from theta times 180 divided by pi. A 0 to 360 degree form is also shown.
When the point is the origin (0, 0) the radius is 0 and the angle is undefined.

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